How do you find the roots for $x^2 + 24 = –11x$ ?

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Answer 1 · 2015-06-05T21:13:10

First add $11x$ to both sides to get

$x^2+11x+24 = 0$

$24 = 3 xx 8$ and $11 = 3 + 8$

So: $x^2+11x+24 = (x+3)(x+8)$

This is based on the general observation that:

$(x+a)(x+b) = x^2 + ax + bx + ab$

$= x^2 + (a+b)x + ab$

Now $(x+3)(x+8) = 0$ when $x=-3$ or $x=-8$ so those are the roots of $x^2+11x+24 = 0$

How do you find the roots for x^2 + 24 = –11xx^2 + 24 = –11x?